The dimensions of the matrix A and B are 3×2 and 2×1, respectively, so the resultant matrix will be of dimension 3×1. The multiplication of the matrices A and B is. The dimensions of the matrix A and B are 1×4 and 4×1, respectively, so the resultant matrix will be of dimension 1×1. Scalar: k(AB)=(kA)B (where k is scalar)Įxample 1: Multiply the following matrices.
Similarly, we can find the multiplication of the matrices with different dimensions. The resultant matrix is: Multiplication of a 2×2 matrix and 2×1 matrix Multiplication of the two 2×2 matrix Multiplication of 3×3 matrix To find the fourth element of the resultant matrix, multiply the second row of matrix A by the second column of matrix B and sum up the product. To find the third element of the resultant matrix, multiply the second row of matrix A by the first column of matrix B and sum up the product. To find the second element of the resultant matrix, multiply the first row of matrix A by the second column of matrix B and sum up the product. To find the first element of the resultant matrix, multiply the first row of matrix A by the first column of matrix B and sum up the product. The resultant matrix will be a 2×2 matrix. Suppose we have two matrices A and B of dimensions 2×3 and 3×2, respectively. Suppose we have a matrix A of m×n dimensions and a matrix B of n×k dimensions, then the resultant matrix will be of m×k dimensions. In matrix multiplication, it is not necessary that both matrices must be a square matrix, as in addition and subtraction. If the condition is not satisfied, the matrix multiplication is not possible. Note: While dealing with the matrix multiplication, remember that the number of columns in the first matrix must be equals to the number of rows in the second matrix. Instead of it, we perform the dot product of the rows and columns.ĭot Product: It is the sum of the product of the matching entries of the two sequences of the numbers. But in matrix multiplication, we do not so. While we do addition or subtraction of matrices, we add or subtract the elements matching with the positions. In this section, we will learn matrix multiplication, its properties, along with its examples. It is a binary operation that performs between two matrices and produces a new matrix. In mathematics, matrix multiplication is different from the multiplication that we perform, generally.
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